The Avengers work as a team to stop supervillain plans, which would have a lasting impact on humankind and the planet. Although their roaster has frequently changed, one thing that remains the same is what they doーwork hard to fight adversaries.
However, although The Avengers is a heroic group who put their lives on the line for humans and the earth, there have been moments where they have taken their efforts too far both against their adversaries and their relationships with other superheroes. Their power can save lives and the earth as they know it. But when that power is used corruptly, it destroys their credibility, relationships, and lives.
10 When The Avengers Tested Spider-Man
In The Amazing Spider-Man Annual #3 (1966), The Avengers put Spider-Man through a test to see if he had what it takes to become an Avenger. Even though Daredevil strongly supported Spider-Man becoming an avenger, they still tested him anyway. They give Spider-Man the assignment of taking The Hulk into custody, and instead of doing that, he lets Hulk go free. And by the end of the story, Spider-Man concludes that working as an Avenger is not the right fit. Peter wants the respect and prestige that comes with being an Avenger (rather than the up and down of being seen as a solo hero one day and a dangerous vigilante the next day).
9 When They Wiped Captain America's Memory
When Iron Man, Professor X, Doctor Strange, Black Bolt, and Mister Fantastic assembled to form The Illuminati (seen via flashback in New Avengers: Illuminati), they intended to gather to discuss future risks that adversaries might pose. But what they may not have known is how much of a risk they'd be to one of their own fellow heroes. In New Avengers: Illuminati (2006) #2, the world faced the risk of invasion and attack in the Multiverse that would have catastrophic impacts.
So, the Illuminati gathered again to try and save the planet. They surmised that to save the world as they knew it, they'd have to destroy the Alternate Earth (but Captain America was vehemently against it, and he told them so). As the team formed a deadly weapon that would wipe out the Alternate Earth, Captain America stood his ground. Their decision to remove Captain America's knowledge was destructive and the opposite of what they claimed to stand for. Tampering with adversary's memories is touchy enough as it is, but to wipe the memory of one of your own to exclude them from your group and its plans show a moral bankruptcy that is hard to accept. It completely soured everything they claim to stand for as individuals and as a group.
8 When They Opposed The X-Men
In Avengers vs. X-Men, Pheonix Force is making its way towards the earth, and Hope Summers is its presumed target host. As the first mutant to be born after M-Day, some believe Summers could save mutantkind, and others believe she could destroy the world. The Avengers were at odds with The X-Men on how to handle this issue safely. While The Avengers believed that the Pheonix Force would end the world as they knew it, The X-Men believed that it would bring about a new era for mutant kind.
Of course, this deep division led to a war between The Avengers and The X-Men that ended with the two groups coming together as Scarlett Witch shifted reality, and Captain America accepted that The Avengers should have done more to help the mutants not be seen so negatively by society. Captain America also vows to form a new Avengers group that would be more inclusive of mutant and human heroes.
7 When They Hunted For Mutants
Set in Earth-11326 (an Age of X alternate reality where the X-Men never formed), Avengers hunting for humans was a troubling moment in their history. In this storyline, the Avengers form as a group 1000 days before hunting mutants (and some members of the Avengers already had mutant-hunting experience that preceded General Frank Castle's mandate to hunt mutants). In this story, instead of being heroes, they are amongst several groups of mutant villains.
6 When They Stood Back As Doctor Strange Partnered With Dark Magic
Doctor Strange was Sorcerer Supreme, and with that great power came great responsibility. It's was his duty to stop magical threats in their tracks, and it was also his responsibility to face off against demons and either overpower them or cast them back to their native dimension. And as a member of the Avengers, it's his and his teammates' job to help protect the planet and the people who inhabit it. So when Doctor Strange decided to make a dark magic pack with an evil being, the Avengers don't seem to put up much of a fight. Their decision to sit back and allow Doctor Strange to work with this evil force was the wrong one, and it renders any good the Avengers tried to do as null and void.
5 When They Attacked A Teenager
When The Avengers encounter the super-powered and seemingly destructive student who has become Starbrand (in Avengers (2013) #7), they go into attack-mode. The Starbrand power has been in the hands of others previously, and it has given the wielder incredible powers. The one wielding the power of Starbrand can destroy a planet to save it. When they arrive at the destroyed school campus, they find the latest incarnation of Starbrand as what appears to be the sole survivor on a college campus. In Avengers (2013) #8, The Avengers act impulsively, with Thor and The Hulk moving to use full-force on the youth (named Kevin Connor) when he gets riled up as they suggest he comes with them for testing.
4 When They Formed A Secret Group
When The Avengers formed The Illuminati, They kept this group a secret from other superhero teams they are part of (such as Mister Fantastic not telling The Fantastic Four and Professor X keeping the group a secret from the X-Men). In New Avengers: Illuminati (2006) #1, readers learn that they formed this secret group to save the world supposedly. One would imagine that they thought their other superhero colleagues were either not smart enough or strong enough to be a part of their group, which is truly a glorified ego trip. Or maybe their other colleagues would tell them how stupid the group actually is, and they'd have to disband. They made so many terrible decisions (such as splitting the infinity gems amongst each other and keeping this secret from superhero friends they claim they would trust with their lives).
3 When They Betrayed Scarlet Witch
It seems impossible that a team that claims to be about community, teamwork, and justice would come together and reach this kind of a consensus. However, after Avengers Disassembled, The Avengers that were left were deeply concerned about the Scarlet Witch and her powers. So, they came together (behind her back) and began brainstorming what should become of Scarlet Witch. And boy, they left nothing off the table. Instead of valuing the life of their teammate, who had been instrumental in helping to save the day on many missions, they actually thought about killing her off. They certainly left respect, morality, and trust completely out of the equation.
2 Banishing The Hulk Into Space
A common theme with The Avengers is that they go behind each other's back to accomplish what other teammates think ought to be done. So, it's not a surprise that The Avengers frequently change their roaster, but what's amazing is that the group itself seems to keep forming (with whomever it welcomes) when the team does not have a good track record when it comes to respecting justice within the team. In the Planet Hulk storyline (found in several issues in The Incredible Hulk). The Hulk finds out that his former teammates banished him to space, thinking he's too much of a risk to stay on earth. The Avenger's planned to kill the Hulk, but he survived the attempt on his life and then came back to earth with a huge army and trashed Manhattan and the people who used to be his team members.
1 When They Took A Break From The Team Behind Captain America's Back
In The Avengers (1963) #16, Wasp, Iron Man, and Giant-Man decide to take a break from The Avengers and bring in Scarlet Witch, Quicksilver, and Hawkeye to take their place. They did this while Captain America left to take care of some business independently and didn't even consult him before bringing on new replacements. This is wrong on two levels: first, it's wrong to take a leave of absence without consulting the entire team and getting a full opinion on the issue. Second, placing replacements of your choosing without consulting the one you left behind to work with them is wrong too.